It's summer. I kneel Kraznys to take control of an attachment card in play. As an example, let's say I took this.

Can I place this attachment on any character I want since Kraznys is saying "card of your choice" in specific, (unlike "Crown of Mereen" that uses the phrase "eligible card of your choice").

If I can place it on Kraznys, I know it will be discarded since its's not following the restriction "Ironborn character only".

OR is this move not legit at all since I must follow the attachments restriction when I place it?

Please use Rules/FaQ references.

OR is this move not legit at all since I must follow the attachments restriction when I place it?

^^This.

The FAQ reference is:

(3.22) Attachment Restrictions

Any attachment that has a restriction (such as "Lord or Lady only" or "attach to an opponent's character") is immediately discarded from play at any time that restriction is not met, regardless of immunity. Such restrictions are constant effects, and the attachment should be immediately discarded any time a restriction is not met including during setup.

The fact that the restrictions are constant effects is what prevents you from playing or moving attachments to ineligible characters in the first place.

You cannot move Support of Saltcliffe to Kraznys for the same reason you cannot play Support of Saltcliffe from your hand on Kraznys.

However, you can take control of Support from Saltcliffe and put it on an opponent's eligible character. After that, you are the only player who can trigger the response. You probably won't want to, but the opponent won't be able to use it either.

The opponent loses access to any triggered effects on the attachment when you take control of it. It doesn't need to move for that to happen.